Monty Hall Problem Simulator

The Monty Hall Problem is as follows. You are on a game show. There are 3 doors, 2 with goats behind them, and 1 with a new car (the goal is to get the new car). The host, Monty, asks you to pick a door. You pick a door. The host then opens a door that you did not pick, revealing a goat. He offers you the choice of staying with the door you picked, or switching to the other unopened door (he offers every contestant this option). Do you stay? Do you change doors? Are you more likely to get the car if you stay or change? Are you just as likely either way? What is your probability of getting the car if you stay? If you change? Many mathematicians got this problem wrong.

Once you're confident in your answer, try simulating the Monty Hall problem. Pick a strategy (switch doors or not), and do ten trials. Do a hundred. Do ten thousand! Try the other strategy. Do the simulation results match your prediction?

Trial Count: Switch doors: Verbose: